The kilogram, also kilogramme, is the base unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering, and commerce worldwide, and is often called a kilo.

The kilogram was originally defined in 1795 as the mass of a litre (cubic decimetre) of water. This was a convenient definition, but hard to replicate precisely. In 1799, a platinum artefact replaced it as a standard mass sample. Later, the International Prototype Kilogram (IPK) remained the standard of the unit of mass for the metric system until 20 May 2019.[1] In spite of best efforts to maintain it, the IPK diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led to efforts to develop measurement technology precise enough to allow replacing the kilogram artefact with a definition based directly on physical fundamental constants.[1] This was achieved in 2018, with a definition in terms of the Planck constant.[1] Thus, the kilogram is now defined in terms of the second and the metre, eliminating the need for the IPK.[2] The new definition was approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018.[3] The Planck constant relates a light particle's energy, and hence mass, to its frequency. The new definition only became possible when instruments were devised to measure the Planck constant with sufficient accuracy based on the IPK definition of the kilogram.

The current definition of the kilogram came into force on 20 May 2019.[4] It defines the Planck constant as exactly 6.62607015×10−34 kg⋅m2⋅s−1, thereby defining the kilogram in terms of the second and the metre.[2] Since the second and metre are defined completely in terms of physical constants, the kilogram is defined in terms of physical constants only.

The first metric system started to be developed in about 1790. The initial mass unit was the grave, which evolved into the kilogram.
The gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimetre of water at the melting point of ice.[5]
The Kilogramme des Archives, manufactured as a prototype in 1799 and from which the International Prototype Kilogram (IPK) was derived in 1875, had a mass equal to the mass of 1 dm3 of water under atmospheric pressure and at the temperature of its maximum density, which is approximately 4 °C.

The kilogram was the last SI unit that was directly defined by an artefact rather than a fundamental physical property that could be independently reproduced in different laboratories.[1] Three other base units (cd, A, mol) and 17 derived units (N, Pa, J, W, C, V, F, Ω, S, Wb, T, H, kat, Gy, Sv, lm, lx) in the SI system are defined in relation to the kilogram, and thus its stability is important. The definitions of only eight other named SI units did not depend on the kilogram: those of temperature (K, °C), time and frequency (s, Hz, Bq), length (m), and angle (rad, sr).[6]

After the International Prototype Kilogram had been found to vary in mass over time relative to its reproductions,[7] the International Committee for Weights and Measures (CIPM) recommended in 2005 that the kilogram be redefined in terms of a fundamental constant of nature. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, h. The decision was originally deferred until 2014; in 2014 it was deferred again until the next meeting.[8] CIPM has proposed[9] revised definitions of the SI base units, for consideration at the 26th CGPM. The formal vote, which took place on 16 November 2018,[10] approved the change.[11]

The avoirdupois (or international)pound, used in both the imperial and US customary systems, is now defined in terms of the kilogram, as 0.453 592 37 kg).[12] Other traditional units of weight and mass around the world are now also defined in terms of the kilogram, making the kilogram the primary standard for virtually all units of mass on Earth.

The kilogram is the only base SI unit with an SI prefix (kilo) as part of its name. The word kilogramme or kilogram is derived from the Frenchkilogramme,[13] which itself was a learned coinage, prefixing the Greek stem of χίλιοιkhilioi "a thousand" to gramma, a Late Latin term for "a small weight", itself from Greek γράμμα.[14]
The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal,[15]
which revised the older system of units introduced by the French National Convention in 1793, where the gravet had been defined as weight (poids) of a cubic centimetre of water, equal to 1/1000 of a grave.[16] In the decree of 1795, the term gramme thus replaced gravet, and kilogramme replaced grave.

The French spelling was adopted in Great Britain when the word was used for the first time in English in 1795,[17][13] with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common.[18][Note 2] UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling.[19]

In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has been used to mean both kilogram[20] and kilometre.[21] While kilo is acceptable in many generalist texts, for example The Economist,[22] its use is typically considered inappropriate in certain applications including scientific, technical and legal writing, where authors should adhere strictly to SI nomenclature.[23][24] When the United States Congress gave the metric system legal status in 1866, it permitted the use of the word kilo as an alternative to the word kilogram,[25] but in 1990 revoked the status of the word kilo.[26]

During the 19th century, the standard system of metric units was the centimetre–gram–second system of units, treating the gram as the fundamental unit of mass and the kilogram simply as a derived unit.
In 1901, however, following the discoveries by James Clerk Maxwell to the effect that electric measurements could not be explained in terms of the three fundamental units of length, mass and time, Giovanni Giorgi proposed a new standard system that would include a fourth fundamental unit to measure quantities in electromagnetism.[27]
In 1935 this was adopted by the IEC as the Giorgi system, now also known as MKS system,[28]
and in 1946 the CIPM approved a proposal to adopt the ampere as the electromagnetic unit of the "MKSA system".[29]:109,110
In 1948 the CGPM commissioned the CIPM "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention".[30] This led to the launch of SI in 1960 and the subsequent publication of the "SI Brochure", which stated that "It is not permissible to use abbreviations for unit symbols or unit names ...".[31][Note 3]
The CGS and MKS systems co-existed during much of the early-to-mid 20th century, but as a result of the decision to adopt the "Giorgi system" as the international system of units in 1960, the kilogram is now the SI base unit for mass, while the definition of the gram is derived from that of the kilogram.

The kilogram is a unit of mass, a property corresponding to the common perception of how "heavy" an object is. Mass is an inertial property; that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity, unless acted upon by a force.

While the weight of an object is dependent on the strength of the local gravitational field, the mass of an object is independent of gravity, as mass is a measure of the quantity of matter. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor; they are "weightless". However, since objects in microgravity still retain their mass and inertia, an astronaut must exert ten times as much force to accelerate a 10‑kilogram object at the same rate as a 1‑kilogram object.

Because at any given point on Earth the weight of an object is proportional to its mass, the mass of an object in kilograms is usually measured by comparing its weight to the weight of a standard mass, whose mass is known in kilograms, using a device called a weighing scale. The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses.

In the following subsections, wherever numeric equalities are shown in concise form—such as 1.85487(14)×1013—the two digits between the parentheses denote the uncertainty at one standard deviation (1σ, the 68% confidence level) in the two least significant digits of the significand.

The International Committee for Weights and Measures (CIPM) approved a redefinition of the SI base units in November 2018 that defines the kilogram by defining the Planck constant to be exactly 6.62607015×10−34 kg⋅m2⋅s−1. This approach effectively defines the kilogram in terms of the second and the metre, and took effect on 20 May 2019.[1][2][32]

In 1960, the metre, previously similarly having been defined with reference to a single platinum-iridium bar with two marks on it, was redefined in terms of an invariant physical constant (the wavelength of a particular emission of light emitted by krypton,[33] and later the speed of light) so that the standard can be independently reproduced in different laboratories by following a written specification.

In October 2010, the CIPM voted to submit a resolution for consideration at the General Conference on Weights and Measures (CGPM), to "take note of an intention" that the kilogram be defined in terms of the Planck constant, h (which has dimensions of energy times time) together with other physical constants.[35][36] This resolution was accepted by the 24th conference of the CGPM[37] in October 2011 and further discussed at the 25th conference in 2014.[38][39] Although the Committee recognised that significant progress had been made, they concluded that the data did not yet appear sufficiently robust to adopt the revised definition, and that work should continue to enable the adoption at the 26th meeting, scheduled for 2018.[38] Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. The Kibble balance (discussed below) is one way do this.

As part of this project, a variety of very different technologies and approaches were considered and explored over many years. They too are covered below. Some of these now-abandoned approaches were based on equipment and procedures that would have enabled the reproducible production of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) using measurement techniques and material properties that are ultimately based on, or traceable to, physical constants. Others were based on devices that measured either the acceleration or weight of hand-tuned kilogram test masses and which expressed their magnitudes in electrical terms via special components that permit traceability to physical constants. All approaches depend on converting a weight measurement to a mass, and therefore require the precise measurement of the strength of gravity in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.

The Kibble balance requires extremely precise measurement of the local gravitational acceleration g in the laboratory, using a gravimeter. For instance when the elevation of the centre of the gravimeter differs from that of the nearby test mass in the Kibble balance, the NIST compensates for Earth's gravity gradient of 309μGal per metre, which affects the weight of a one-kilogram test mass by about 316μg/m.

In April 2007, the NIST's implementation of the Kibble balance demonstrated a combined relative standard uncertainty (CRSU) of 36μg.[40][Note 4] The UK's National Physical Laboratory's Kibble balance demonstrated a CRSU of 70.3μg in 2007.[41] That Kibble balance was disassembled and shipped in 2009 to Canada's Institute for National Measurement Standards (part of the National Research Council), where research and development with the device could continue.

The local gravitational acceleration g is measured with exceptional precision with the help of a laser interferometer. The laser's pattern of interference fringes—the dark and light bands above—blooms at an ever-faster rate as a free-falling corner reflector drops inside an absolute gravimeter. The pattern's frequency sweep is timed by an atomic clock.

Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration g, are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, g varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see Earth's gravity). There are also slight seasonal variations in g at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape caused by the Moon and the Sun. Although g would not be a term in the definition of the kilogram, it would be crucial in the process of measurement of the kilogram when relating energy to power. Accordingly, g must be measured with at least as much precision and accuracy as are the other terms, so measurements of g must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, g is measured using dropping-mass absolute gravimeters that contain an iodine-stabilised helium–neon laserinterferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium atomic clock. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt‑10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8 ppb of 9.80101644 m/s2.[42]

The virtue of electronic realisations like the Kibble balance is that the definition and dissemination of the kilogram no longer depends upon the stability of kilogram prototypes, which must be very carefully handled and stored. It frees physicists from the need to rely on assumptions about the stability of those prototypes. Instead, hand-tuned, close-approximation mass standards can simply be weighed and documented as being equal to one kilogram plus an offset value. With the Kibble balance, while the kilogram is delineated in electrical and gravity terms, all of which are traceable to invariants of nature; it is defined in a manner that is directly traceable to three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the metre. By fixing the Planck constant, the definition of the kilogram depends in addition only on the definitions of the second and the metre. The definition of the second depends on a single defined physical constant: the ground state hyperfine splitting frequency of the caesium 133 atom Δν(133Cs)hfs. The metre depends on the second and on an additional defined physical constant: the speed of lightc. With the kilogram redefined in this manner, physical objects such as the IPK are no longer be part of the definition, but instead become transfer standards.

Scales like the Kibble balance also permit more flexibility in choosing materials with especially desirable properties for mass standards. For instance, Pt‑10Ir could continue to be used so that the specific gravity of newly produced mass standards would be the same as existing national primary and check standards (≈21.55g/ml). This would reduce the relative uncertainty when making mass comparisons in air. Alternatively, entirely different materials and constructions could be explored with the objective of producing mass standards with greater stability. For instance, osmium-iridium alloys could be investigated if platinum's propensity to absorb hydrogen (due to catalysis of VOCs and hydrocarbon-based cleaning solvents) and atmospheric mercury proved to be sources of instability. Also, vapor-deposited, protective ceramic coatings like nitrides could be investigated for their suitability for chemically isolating these new alloys.

The challenge with Kibble balances is not only in reducing their uncertainty, but also in making them truly practical realisations of the kilogram. Nearly every aspect of Kibble balances and their support equipment requires such extraordinarily precise and accurate, state-of-the-art technology that—unlike a device like an atomic clock—few countries would currently choose to fund their operation. For instance, the NIST's Kibble balance used four resistance standards in 2007, each of which was rotated through the Kibble balance every two to six weeks after being calibrated in a different part of NIST headquarters facility in Gaithersburg, Maryland. It was found that simply moving the resistance standards down the hall to the Kibble balance after calibration altered their values 10ppb (equivalent to 10μg) or more.[43] Present-day technology is insufficient to permit stable operation of Kibble balances between even biannual calibrations. When the new definition takes effect, it is likely there will only be a few—at most—Kibble balances initially operating in the world.

Several alternative approaches to redefining the kilogram that were fundamentally different from the Kibble balance were explored to varying degrees, with some abandoned. The Avogadro project, in particular, was important for the 2018 redefinition decision because it provided an accurate measurement of the Planck constant that was consistent with and independent of the Kibble balance method.[44] The alternative approaches included:

Achim Leistner at the Australian Centre for Precision Optics (ACPO) is holding a 1kg, single-crystal silicon sphere for the Avogadro project. These spheres are among the roundest man-made objects in the world. If the best of these spheres were scaled to the size of Earth, its high point—a continent-size area—would rise to a maximum elevation of 2.4 metres above "sea level".[Note 5]

Another Avogadro constant-based approach, known as the International Avogadro Coordination's Avogadro project, would define and delineate the kilogram as a 93.6mm diameter sphere of silicon atoms. Silicon was chosen because a commercial infrastructure with mature processes for creating defect-free, ultra-pure monocrystalline silicon already exists to service the semiconductor industry. To make a practical realisation of the kilogram, a silicon boule (a rod-like, single-crystal ingot) would be produced. Its isotopic composition would be measured with a mass spectrometer to determine its average relative atomic mass. The boule would be cut, ground, and polished into spheres. The size of a select sphere would be measured using optical interferometry to an uncertainty of about 0.3nm on the radius—roughly a single atomic layer. The precise lattice spacing between the atoms in its crystal structure (≈192pm) would be measured using a scanning X-ray interferometer. This permits its atomic spacing to be determined with an uncertainty of only three parts per billion. With the size of the sphere, its average atomic mass, and its atomic spacing known, the required sphere diameter can be calculated with sufficient precision and low uncertainty to enable it to be finish-polished to a target mass of one kilogram.

Experiments are being performed on the Avogadro Project's silicon spheres to determine whether their masses are most stable when stored in a vacuum, a partial vacuum, or ambient pressure. However, no technical means currently exist to prove a long-term stability any better than that of the IPK's, because the most sensitive and accurate measurements of mass are made with dual-panbalances like the BIPM's FB‑2 flexure-strip balance (see § External links, below). Balances can only compare the mass of a silicon sphere to that of a reference mass. Given the latest understanding of the lack of long-term mass stability with the IPK and its replicas, there is no known, perfectly stable mass artefact to compare against. Single-panscales, which measure weight relative to an invariant of nature, are not precise to the necessary long-term uncertainty of 10–20 parts per billion. Another issue to be overcome is that silicon oxidises and forms a thin layer (equivalent to 5–20 silicon atoms deep) of silicon dioxide (quartz) and silicon monoxide. This layer slightly increases the mass of the sphere, an effect that must be accounted for when polishing the sphere to its finished size. Oxidation is not an issue with platinum and iridium, both of which are noble metals that are roughly as cathodic as oxygen and therefore don't oxidise unless coaxed to do so in the laboratory. The presence of the thin oxide layer on a silicon-sphere mass prototype places additional restrictions on the procedures that might be suitable to clean it to avoid changing the layer's thickness or oxide stoichiometry.

All silicon-based approaches would fix the Avogadro constant but vary in the details of the definition of the kilogram. One approach would use silicon with all three of its natural isotopes present. About 7.78% of silicon comprises the two heavier isotopes: 29Si and 30Si. As described in § Carbon-12 below, this method would define the magnitude of the kilogram in terms of a certain number of 12C atoms by fixing the Avogadro constant; the silicon sphere would be the practical realisation. This approach could accurately delineate the magnitude of the kilogram because the masses of the three silicon nuclides relative to 12C are known with great precision (relative uncertainties of 1ppb or better). An alternative method for creating a silicon sphere-based kilogram proposes to use isotopic separation techniques to enrich the silicon until it is nearly pure 28Si, which has a relative atomic mass of 27.9769265325(19).[45] With this approach, the Avogadro constant would not only be fixed, but so too would the atomic mass of 28Si. As such, the definition of the kilogram would be decoupled from 12C and the kilogram would instead be defined as ​1000⁄27.9769265325 ⋅ 6.02214179×1023 atoms of 28Si (≈ 35.74374043 fixed moles of 28Si atoms). Physicists could elect to define the kilogram in terms of 28Si even when kilogram prototypes are made of natural silicon (all three isotopes present). Even with a kilogram definition based on theoretically pure 28Si, a silicon-sphere prototype made of only nearly pure 28Si would necessarily deviate slightly from the defined number of moles of silicon to compensate for various chemical and isotopic impurities as well as the effect of surface oxides.[46]

Though not offering a practical realisation, this definition would precisely define the magnitude of the kilogram in terms of a certain number of carbon‑12 atoms. Carbon‑12 (12C) is an isotope of carbon. The mole is currently defined as "the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon‑12". Thus, the current definition of the mole requires that ​1000⁄12 moles (​831⁄3 mol) of 12C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is experimentally determined, and the current best estimate of its value is 6.02214076×1023 entities per mole.[47] This new definition of the kilogram proposed to fix the Avogadro constant at precisely 6.02214X×1023 mol−1 with the kilogram being defined as "the mass equal to that of ​1000⁄12 ⋅ 6.02214X×1023 atoms of 12C".

The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the Planck constant. That relative standard uncertainty has been 50parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposal would be that the uncertainty in the mass of a 12C atom—and the magnitude of the kilogram—could be no better than the current 50ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram would be subject to future refinement as improved measurements of the value of the Planck constant become available; electronic realisations of the kilogram would be recalibrated as required. Conversely, an electronic definition of the kilogram (see § Electronic approaches, below), which would precisely fix the Planck constant, would continue to allow ​831⁄3 moles of 12C to have a mass of precisely one kilogram but the number of atoms comprising a mole (the Avogadro constant) would continue to be subject to future refinement.

A variation on a 12C-based definition proposes to define the Avogadro constant as being precisely 844468893 (≈6.02214162×1023) atoms. An imaginary realisation of a 12-gram mass prototype would be a cube of 12C atoms measuring precisely 84446889 atoms across on a side. With this proposal, the kilogram would be defined as "the mass equal to 844468893× ​831⁄3 atoms of 12C."[48][Note 6]

Another Avogadro-based approach, ion accumulation, since abandoned, would have defined and delineated the kilogram by precisely creating new metal prototypes on demand. It would have done so by accumulating gold or bismuthions (atoms stripped of an electron) and counting them by measuring the electric current required to neutralise the ions. Gold (197Au) and bismuth (209Bi) were chosen because they can be safely handled and have the two highest atomic masses among the mononuclidic elements that are stable (gold) or effectively so (bismuth).[Note 7] See also Table of nuclides.

With a gold-based definition of the kilogram for instance, the relative atomic mass of gold could have been fixed as precisely 196.9665687, from the current value of 196.9665687(6). As with a definition based upon carbon‑12, the Avogadro constant would also have been fixed. The kilogram would then have been defined as "the mass equal to that of precisely ​1000⁄196.9665687 ⋅ 6.02214179×1023 atoms of gold" (precisely 3,057,443,620,887,933,963,384,315 atoms of gold or about 5.07700371 fixed moles).

In 2003, German experiments with gold at a current of only 10 μA demonstrated a relative uncertainty of 1.5%.[50] Follow-on experiments using bismuth ions and a current of 30mA were expected to accumulate a mass of 30g in six days and to have a relative uncertainty of better than 1 ppm.[51] Ultimately, ion‑accumulation approaches proved to be unsuitable. Measurements required months and the data proved too erratic for the technique to be considered a viable future replacement to the IPK.[52]

Among the many technical challenges of the ion-deposition apparatus was obtaining a sufficiently high ion current (mass deposition rate) while simultaneously decelerating the ions so they could all deposit onto a target electrode embedded in a balance pan. Experiments with gold showed the ions had to be decelerated to very low energies to avoid sputtering effects—a phenomenon whereby ions that had already been counted ricochet off the target electrode or even dislodged atoms that had already been deposited. The deposited mass fraction in the 2003 German experiments only approached very close to 100% at ion energies of less than around 1 eV (<1km/s for gold).[50]

If the kilogram had been defined as a precise quantity of gold or bismuth atoms deposited with an electric current, not only would the Avogadro constant and the atomic mass of gold or bismuth have to have been precisely fixed, but also the value of the elementary charge (e), likely to 1.60217X×10−19C (from the currently recommended value of 1.602176634×10−19 C[53]). Doing so would have effectively defined the ampere as a flow of ​1⁄1.60217X×10−19 electrons per second past a fixed point in an electric circuit. The SI unit of mass would have been fully defined by having precisely fixed the values of the Avogadro constant and elementary charge, and by exploiting the fact that the atomic masses of bismuth and gold atoms are invariant, universal constants of nature.

Beyond the slowness of making a new mass standard and the poor reproducibility, there were other intrinsic shortcomings to the ion‑accumulation approach that proved to be formidable obstacles to ion-accumulation-based techniques becoming a practical realisation. The apparatus necessarily required that the deposition chamber have an integral balance system to enable the convenient calibration of a reasonable quantity of transfer standards relative to any single internal ion-deposited prototype. Furthermore, the mass prototypes produced by ion deposition techniques would have been nothing like the freestanding platinum-iridium prototypes currently in use; they would have been deposited onto—and become part of—an electrode imbedded into one pan of a special balance integrated into the device. Moreover, the ion-deposited mass wouldn't have had a hard, highly polished surface that can be vigorously cleaned like those of current prototypes. Gold, while dense and a noble metal (resistant to oxidation and the formation of other compounds), is extremely soft so an internal gold prototype would have to be kept well isolated and scrupulously clean to avoid contamination and the potential of wear from having to remove the contamination. Bismuth, which is an inexpensive metal used in low-temperature solders, slowly oxidises when exposed to room-temperature air and forms other chemical compounds and so would not have produced stable reference masses unless it was continually maintained in a vacuum or inert atmosphere.

A magnet floating above a superconductor bathed in liquid nitrogen demonstrates perfect diamagnetic levitation via the Meissner effect. Experiments with an ampere-based definition of the kilogram flipped this arrangement upside-down: an electric field accelerated a superconducting test mass supported by fixed magnets.

This approach would define the kilogram as "the mass which would be accelerated at precisely 2×10−7 m/s2 when subjected to the per-metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed one metre apart in vacuum, through which flow a constant current of ​1⁄1.60217×10^−19 elementary charges per second".

Effectively, this would define the kilogram as a derivative of the ampere rather than the present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would specify elementary charge (e) as precisely 1.60217×10^−19coulomb rather than the current recommended value of 1.602176634×10−19 C.[53] It would necessarily follow that the ampere (one coulomb per second) would also become an electric current of this precise quantity of elementary charges per second passing a given point in an electric circuit.
The virtue of a practical realisation based upon this definition is that unlike the Kibble balance and other scale-based methods, all of which require the careful characterisation of gravity in the laboratory, this method delineates the magnitude of the kilogram directly in the very terms that define the nature of mass: acceleration due to an applied force. Unfortunately, it is extremely difficult to develop a practical realisation based upon accelerating masses. Experiments over a period of years in Japan with a superconducting, 30g mass supported by diamagnetic levitation never achieved an uncertainty better than ten parts per million. Magnetic hysteresis was one of the limiting issues. Other groups performed similar research that used different techniques to levitate the mass.[54][55]

Because SI prefixes may not be concatenated (serially linked) within the name or symbol for a unit of measure, SI prefixes are used with the unit gram, not kilogram, which already has a prefix as part of its name.[56] For instance, one-millionth of a kilogram is 1mg (one milligram), not 1μkg (one microkilogram).

The microgram is typically abbreviated "mcg" in pharmaceutical and nutritional supplement labelling, to avoid confusion, since the "μ" prefix is not always well recognised outside of technical disciplines.[Note 9] (The expression "mcg" is also the symbol for an obsolete CGS unit of measure known as the "millicentigram", which is equal to 10μg.)

In the United Kingdom, because serious medication errors have been made from the confusion between milligrams and micrograms when micrograms has been abbreviated, the recommendation given in the Scottish Palliative Care Guidelines is that doses of less than one milligram must be expressed in micrograms and that the word microgram must be written in full, and that it is never acceptable to use "mcg" or "μg".[57]

The hectogram (100 g) is a very commonly used unit in the retail food trade in Italy, usually called an etto, short for ettogrammo, the Italian for hectogram.[58][59][60]

The former standard spelling and abbreviation "deka-" and "dk" produced abbreviations such as "dkm" (dekametre) and "dkg" (dekagram).[61] The abbreviation "dkg" (10 g) is still used in parts of central Europe in retail for some foods such as cheese and meat.[citation needed]

The unit name megagram is rarely used, and even then typically only in technical fields in contexts where especially rigorous consistency with the SI standard is desired. For most purposes, the name tonne is instead used. The tonne and its symbol, "t", were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPM for use with the SI. According to the BIPM, "In English speaking countries this unit is usually called 'metric ton'."[62] The unit name megatonne or megaton (Mt) is often used in general-interest literature on greenhouse gas emissions, whereas the equivalent unit in scientific papers on the subject is often the teragram (Tg).

^The combined relative standard uncertainty (CRSU) of these measurements, as with all other tolerances and uncertainties in this article unless otherwise noted, are at one standard deviation (1σ), which equates to a confidence level of about 68%; that is to say, 68% of the measurements fall within the stated tolerance.

^The sphere shown in the photograph has an out-of-roundness value (peak to valley on the radius) of 50nm. According to ACPO, they improved on that with an out-of-roundness of 35nm. On the 93.6mm diameter sphere, an out-of-roundness of 35nm (deviation of ±17.5nm from the average) is a fractional roundness (∆r/r) = 3.7×10−7. Scaled to the size of Earth, this is equivalent to a maximum deviation from sea level of only 2.4m. The roundness of that ACPO sphere is exceeded only by two of the four fused-quartz gyroscope rotors flown on Gravity ProbeB, which were manufactured in the late 1990s and given their final figure at the W.W. Hansen Experimental Physics Lab at Stanford University. Particularly, "Gyro 4" is recorded in the Guinness database of world records (their database, not in their book) as the world's roundest man-made object. According to a published report (221kB PDF, hereArchived February 27, 2008, at the Wayback Machine) and the GP‑B public affairs coordinator at Stanford University, of the four gyroscopes onboard the probe, Gyro4 has a maximum surface undulation from a perfect sphere of 3.4±0.4nm on the 38.1mm diameter sphere, which is a ∆r/r = 1.8×10−7. Scaled to the size of Earth, this is equivalent to an deviation the size of North America rising slowly up out of the sea (in molecular-layer terraces 11.9cm high), reaching a maximum elevation of 1.14±0.13m in Nebraska, and then gradually sloping back down to sea level on the other side of the continent.

^The proposal originally was to redefine the kilogram as the mass of 844468863 carbon-12 atoms.[49] The value 84446886 had been chosen because it has a special property; its cube (the proposed new value for the Avogadro constant) is divisible by twelve. Thus with that definition of the kilogram, there would have been an integer number of atoms in one gram of 12C: 50184508190229061679538 atoms. The uncertainty in the Avogadro constant has narrowed considerably since this proposal was first submitted to American Scientist for publication. The 2014 CODATA value for the Avogadro constant (6.022140857(74)×1023) has a relative standard uncertainty of 12 parts per billion and the cube root of this number is 84446885.41(35), i.e. there are no integers within the range of uncertainty.

^In 2003, the same year the first gold-deposition experiments were conducted, physicists found that the only naturally occurring isotope of bismuth, 209Bi, is actually very slightly radioactive, with the longest known radioactive half-life of any naturally occurring element that decays via alpha radiation—a half-life of (19±2)×1018 years. As this is 1.4 billion times the age of the universe, 209Bi is considered a stable isotope for most practical applications (those unrelated to such disciplines as nucleocosmochronology and geochronology). In other terms, 99.999999983% of the bismuth that existed on Earth 4.567 billion years ago still exists today. Only two mononuclidic elements are heavier than bismuth and only one approaches its stability: thorium. Long considered a possible replacement for uranium in nuclear reactors, thorium can cause cancer when inhaled because it is over 1.2billion times more radioactive than bismuth. It also has such a strong tendency to oxidise that its powders are pyrophoric. These characteristics make thorium unsuitable in ion-deposition experiments. See also Isotopes of bismuth, Isotopes of gold and Isotopes of thorium.

^Gramme, le poids absolu d'un volume d'eau pure égal au cube de la centième partie du mètre, et à la température de la glace fondante; The term poids absolu was at the time used alongside masse for the concept of "mass" (which latter term had first been introduced in its strict physical sense in English in 1704).
See e.g. Mathurin Jacques Brisson, Dictionnaire raisonné de toutes les parties de la Physique, Volland, 1787, p. 401.

^Wood, B. (November 3–4, 2014). "Report on the Meeting of the CODATA Task Group on Fundamental Constants"(PDF). BIPM. p. 7. [BIPM director Martin] Milton responded to a question about what would happen if ... the CIPM or the CGPM voted not to move forward with the redefinition of the SI. He responded that he felt that by that time the decision to move forward should be seen as a foregone conclusion.

^Fowlers, HW; Fowler, FG (1964). The Concise Oxford Dictionary. Oxford: The Clarendon Press.
Greek γράμμα (as it were γράφ-μα, Doric γράθμα) means "something written, a letter", but it came to be used as a unit of weight, apparently equal to 1/24 of an ounce (1/288 of a libra, which would correspond to about 1.14 grams in modern units), at some time during Late Antiquity. French gramme was adopted from Latin gramma, itself quite obscure, but found in the Carmen de ponderibus et mensuris (8.25) attributed by Remmius Palaemon (fl. 1st century), where it is the weight of two oboli (Charlton T. Lewis, Charles Short, A Latin Dictionarys.v. "gramma", 1879).
Henry George Liddell. Robert Scott. A Greek-English Lexicon (revised and augmented edition, Oxford, 1940) s.v. γράμμα, citing the 10th-century work Geoponica and a 4th-century papyrus edited in L. Mitteis, Griechische Urkunden der Papyrussammlung zu Leipzig, vol. i (1906), 62 ii 27.

^R. Steiner, No FG-5?, NIST, Nov 30, 2007. "We rotate between about 4 resistance standards, transferring from the calibration lab to my lab every 2–6 weeks. Resistors do not transfer well, and sometimes shift at each transfer by 10 ppb or more."

^Lim, XiaoZhi (November 16, 2018). "The Kilogram Is Dead. Long Live the Kilogram!". The New York Times. Avogadro’s constant and the Planck constant are intertwined in the laws of physics. Having measured Avogadro’s constant, Dr. Bettin could derive the Planck constant. And with a precise measure of the Planck constant, he could validate the results of Dr. Kibble’s work, and vice versa.